Archive ouverte HAL – Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

Grégoire Misguich 1 Nicolas Pavloff 2 Vincent Pasquier 1

Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier. Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point. SciPost Physics, SciPost Foundation, 2019, 7 (2), ⟨10.21468/SciPostPhys.7.2.025⟩. ⟨hal-02295825⟩

We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

  • 1. IPHT - Institut de Physique Théorique - UMR CNRS 3681
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques